Curved finger boards for stringed musical instruments



Nov. 18, 1969. A. R. FISHER 3,478,631

CURVED FINGER BOARDS FOR STRINGED MUSICAL INSTRUMENTS Filed Dec. 5, 19682 Sheets-Sheet l F'lG.l

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F'IG.4 m5? A T TORNE Y Nov. 18, 1969 A. R. FISHER 3,478,631

CURVED FINGER BOARDS FOR STRINGED MUSICAL INSTRUMENTS United StatesPatent O US. Cl. 84-293 2 Claims ABSTRACT OF THE DISCLOSURE A fingerboard for stringed musical instruments which has a face longitudinallycurved on a logarithmic spiral so that a string when pressed against thefinger board at any point along its length will make the same angle withthe finger board at each point.

REFERENCE TO RELATED APPLICATION This application is acontinuation-in-part of my copending patent application which is nowabandoned. Title: Curved Finger Board For Stringed Musical Instruments;Serial No.: 640,674; Filing Date: May 23, 1967.

GENERAL DESCRIPTION OF THE INVENTION This invention relates to fingerboards for stringed musical instruments wherein the finger board has alongitudinally curved face portion so that it lies closer to the stringsat the nut and bridge and allows greater amplitude of string vibrationmidway between the nut and bridge. This curvature is a logarithmicspiral originating at the point where the string crosses the bridge sothat the active portion of a string pressed against said finger board atany point along its length makes the same angle with the finger board ateach point.

Stringed musical instruments such as violins, violas, cellos, doublebasses, banjos, mandolins, guitars, etc. generally have longitudinallystraight finger boards against which the strings are pressed by themusicians fingers l shorten the length of a vibrating string to raisethe pitch of the emitted sound. These straight finger boards are set onan angle to the strings leading away from the strings as the fingerboard extends from the nut toward the bridge or anchor means. As theyapproach the bridge the straight finger boards are so far from thestrings that the strings cannot be pressed against them and they areshortened to a usable length.

In the case of longitudinally straight finger boards, the strings aremost diflicult to depress against the finger board adjacent their pointsof suspension at the nut and the bridge and least diflicult to depressagainst the finger board in the positions midway between the nut and thebridge because the midway positions are remote from the points ofsuspension of the strings. The diificulty of depressing the stringsadjacent their points of suspension can make playing unnecessarilytiring and strenuous.

Also the strings vibrate with maximum amplitude at the positions midwaybetween the points of suspension small magnitude and is unideal in shapeso that the objections remain unsolved.

With the foregoing in view it is an object of the invention to provide acurved finger board which lies ideally close to the strings adjacenttheir points of suspension so that it is easier to depress the stringsagainst the finger board adjacent their points of suspension. The factthat the strings are easier to depress to the finger board near thebridge increases the usable length of the finger board.

In this invention the constant angle between the string and the fingerboard at any point at which the string is pressed, establishes aproportionality between the maximum allowed amplitude of vibration andthe active length of string. As a result, any active length of string,when plucked to vibrate at maximum amplitude, undergoes the same strainand hence the same stress. This ensures a constant plucking force forany active length of string plucked to vibrate at its maximum amplitude.The tendency to unexpectedly snap the string against the finger board isthereby minimized. The logarithmic spiral curve necessary to provide theconstant angle between the string and finger board is therefore theideal shape.

A constant plucking force applied to a string whose amplitude isproportional to its active length, will produce an energy input to thestring that is inversely proportional to the frequency of emitted sound.As applied to the double bass, which produces low frequency sound, thisfeature results in a constant subjective loudness.

In another form of the invention the logarithmic spiral curve is applieddirectly to the neck portion of the instrument instead of to a separatefinger board.

In another form of the invention frets are positioned on a logarithmicspiral curve so that the top contact surfaces of the frets describe thecurve whether the supporting neck or board is curved or straight.

BRIEF DESCRIPTION OF THE FIGURES OF THE DRAWINGS FIG. 1 is a sideelevational view of a stringed instrument equipped with a longitudinallycurved finger board.

FIG. 2 is a side elevational view of the curved finger board seen inFIG. 1 separate from the instrument.

FIG. 3 is a face elevational view of the device seen in FIG. 2.

FIG. 4 is an end elevational view of the device seen in FIG. 2 taken onthe line 4-4 thereof showing a transversely curving face on the fingerboard.

FIG. 5 is a side elevational view of a curved finger board equipped withfrets.

FIG. 6 is an end elevational view of the device seen in FIG. 5 taken onthe line 66 thereof showing a transversely flat face on the fingerboard.

FIGS. 7 and 8 are side elevational views of the device seen in FIG. 1with the string pressed to the finger board at different points showingthat the same angle a is formed at every point.

FIG. 9 is a graph illustrating an assumed relationship of plucking forceto vibration amplitude.

FIG. 10 is a graph of standard loudness level contours for the humanear, incorporating a field of lines showing constancy of loudness for adouble bass incorporating the invention.

PARTICULAR DESCRIPTION OF THE INVENTION Referring now to the drawingswherein like numerals refer to like and corresponding parts throughoutthe several views, the longitudinally curved finger board shown thereinto illustrate the invention, FIGS. 1-4, comprises a finger board 10mounted to the neck portion of a musical instrument 11 having strings12, a nut 13, and a bridge 17. The strings are suspended over the nut 13and bridge 17. The finger board 10 has opposite ends 14 and 15 and aface 16 curving inwardly lengthwise from the opposite ends 14 and 15.The face 16 at the ends 14 and 15 is closer to the strings 12 adjacentthe nut 13 and bridge 17 respectively relative to a straight fingerboard. The face 16 intermediate the ends 14 and 15 is farther away fromthe strings 12 due to the face 16 curving lengthwise inwardly relativeto a straight finger board. The broken line 18 of FIG. 2 may be regardedas the plane of the face of a straight .finger board for comparison. Thebroken lines 19 and 20 of FIG. 1 may be regarded as the maximumamplitude of string vibration with a straight finger board whereas thedotted line 21 illustrates the increased amplitude of vibration possiblewith the curved finger board 10. It is to be noted that the end 15extends to a point closely adjacent the bridge 17 and also closelyadjacent the strings 12. This is only possible with the curved fingerboard.

It will be apparent that the strings 12 adjacent the nut 13 and bridge17 may be more easily pressed against the face 16 of the curved fingerboard 10 as the face 16 lies closer to the strings 12 adjacent the nut13 and bridge 17 compared to a straight finger board.

The face 16a of the finger board 10a may be equipped with frets 22,FIGS. and 6. Also the face 16 may be transversely curved as seen in FIG.4 or the face 16w may be transversely straight as seen in FIG. 6. Alsothe top contact surfaces of the frets 22 may lie on a curve without thesupporting board lying on a curve. By top contact surface is meant theedge of the fret that the string is pressed against.

Throughout this disclosure the terms active portion and active lengthrefer to that portion of the spring capable of vibrating to producesound. In FIG. 7 these terms refer to the length of string between pointA at which the hand presses it, and the bridge 17. In FIG. 8 the termsrefer to the length of string between point B and the bridge 17. Theterms vibrating portion and vibrating length, as sometimes used forclarity, refer to the identical part of the string that the aforesaidterms refer to. A string is said to be open when it is not pressed tothe finger board at any point, so that its active portion is the lengthof string between the end 14 of the finger board, and the bridge 17.

FIGS. 7 and 8 illustrate how the magnitude of angle formed between thestring and the finger board is the same at every point at which saidstring is pressed to said finger board. The magnitude of the angle itformed between the active portion of the string 12a and a line 26tangent to the finger board at the point A at which said string ispressed to said finger board is the same as the magnitude of the angleor for-med between the active portion of the string 12b.and a line 28tangent to said finger board at any other point B at which said stringis pressed to said finger board. The open string 12 shown in FIG. 1 alsoforms the same magnitude of angle with said finger board at the end 14.

It is a property of a logarithmic spiral curve that a straight linedrawn from the origin of said curve to a point on said curve will forman angle with a line tangent to said curve at said point, this anglebeing equal to that formed between any other straight line drawn fromsaid origin of said curve and the tangent to said curve at the pointwhere said other straight line intersects said curve.

The constant angle at between the string and the line tangent to thefinger board at the point where said string is pressed to said fingerboard is therefore achieved by incorporating a logarithmic spiralcurvature to the face 16. The origin of said spiral is at the point 23at which the string 12 crosses the bridge 17. The logarithmic spiralproceeds from the point 23 along the imaginary line 24 to the end of thefinger board 10 and then forms the longitudinal curvature of the face 16of said finger board. The angle a between the active portion of thestring and a line tangent to the finger board at the point where saidstring is pressed to said finger board will hereinafter be referred toas the angle between the string and the finger board.

The following equation establishes the logarithmic spiral shape of theface of the finger board:

d=distance of face of finger board from the open string 12 at any pointalong said string.

r=distance along the string, from the point where d is measured, to thepoint 23 where said string crosses the bridge.

a=desired angle to be formed between the string and the finger board atevery point on said finger board to which said string is pressed.

ln=natural logarithm.

t=length of the open string.

The constant angle a formed between the string 12 and the finger board10 at every point of depression establishes a fixed proportionalitybetween the vibrating length of said string and the maximum amplitude ofvibration of said string without said string hitting said finger board.The vibrating length of the string 12a divided by its maximum amplitudeof vibration C equals any other vibrating length of the string 12bdivided by its maximum amplitude of vibration D. The same applies to theopen string so that the locus 21 of the string 12 vibrating at itsmaximum amplitude contains a total included angle of 2X0; at each end.Similarly the locus 30 of the string 12a vibrating at its maximumamplitude contains a total included angle of 2 a at each end. Similarlyany other locus 32 of the string 12b vibrating at its maximum amplitudecontains a total included angle of 2X0: at each end. Therefore all lociof maximum amplitudes are geometrically similar.

The foregoing establishes that for any string on the instrument 11 theunit strain of the string when vibrating at maximum amplitude is thesame for any vibrating length of said string. The unit strain in thevibrating portion 21 of the open string 12 is the same magnitude as theunit strain in the vibrating portion 30 of the string 12a and is thesame magnitude as the unit strain in any other vibrating portion 32 ofthe string 12b when said string is vibrating at maximum amplitude ineach case.

It is essential for producing accurate pitches that a string beconstructed of homogeneous material and that it be constant in crosssection along its length. This also ensures that a constant unit strainof one value will have associated with it a unit stress of only onevalue for the entire length of the string. Therefore, the unit stress inthe vibrating portion 21 of the open string 12 is the same magnitude asthe unit stress in the vibrating portion 30 of the string 12a, and isthe same magnitude as the unit stress in any other vibrating portion 32of the string 12b when said string is vibrating at maximum amplitude ineach case.

It has been established that the string cross section is constant, andthat for any active length of string vibrating at maximum amplitude theunit stress and angle a are constant, Therefore the longitudinal forcepresent in the string when said string is in the position of maximumamplitude is the same for any vibrating length of string. For simplicityit will be assumed that the string is always plucked at the longitudinalmid-point of its active portion. From the foregoing it can be deducedthat the force requred from the plucking hand to pluck the string toproduce a vibration at maximum amplitude is the same magnitude for anyactive length of string. The plucking force required to vibrate the openstring '12 at its maximum amplitude 21 is the same magnitude as theplucking force required to vibrate the active portion of the string atits maximum amplitude 30, and is the same magnitude as the pluckingforce required to vibrate any other active portion of the string 12b atits maximum amplitude 32. When the musician has learned what thisconstant maximum plucking force is for each string, he will less oftensnap the string against the finger board unexpectedly because ofplucking too hard. 7

As the plucking hand deflects the string in the act of plucking, therate of rise 34 of force in the string 12a is not necessarily a straightline function but may be related to string amplitude in any complexmanner as shown by the curved line 34. The properties of the string andthe geometric similarity of the loci of maximum vibration amplitudes ofany active length of said string having been established, it logicallyfollows that the rate of rise 36 of plucking force in any other activelength of the string 12b will occur in a manner similar to the rate ofrise 34 of plucking force in the active length of the string 12a, butthat the rate of rise must be inversely proportional to the activelength of the string. This is equivalent to stating that the distancesof curves 34 and 36 from the vertical 0-line in FIG. 9, as measuredalong any horizontal line, are proportional to the amplitudes C and Drespectively and therefore are proportional to the active lengths ofstring 12a and 12b respectively. Therefore, for the constant maximumplucking force established to occur for all active lengths of stringvibrating at maximum amplitude, the areas under the curves areproportional to the active lengths of string. The active length of thestring 12a divided by the .area under the curve 34 equals any otheractive length of the string 12b divided by the area under its curve 36.

Since:

Energy=j (forcexds) where s=distance the areas under the curves of FIG.9 are proportional to the energy imparted to the string in the act ofplucking. In summary, when the string is plucked to vibrate at itsmaximum amplitude allowed by the logarithmic spiral curvature of thefinger board, the energy imparted to said string is proportional to theactive length of said string.

The science of acoustics has been proven that the frequency of vibrationof a string is inversely proportional to its vibrating length. Thereforewhen the string is plucked to vibrate at its maximum amplitude allowedby the logarithmic spiral curvature of the finger board, the energyimparted to said string is inversely proportional to the frequencyproduced by the vibrating length of said string. The frequency is thepitch of the emitted sound. Dilferent pitches are heard by the ear asdifferent notes.

In any well-constructed musical instrument any two notes of differentpitch, but plucked with the same amount of force, will haveapproximately the same duration of sound. The conversion of pluckingenergy into sound energy after the plucking hand releases the stringwill occur in about the same time interval for all pitches. Therefore,when the string is plucked to vibrate at its maximum amplitude allowedby the logarithmic spiral curvature of the finger board, the soundenergy imparted to the air per unit time is inversely proportional tothe frequency produced by the vibrating length of said sting.

Energy per unit of time is power, which can be expressed in many kindsof units including microwatts. With reference to the scale on its righthand side, FIG. 10 shows the relationship of sound power to frequencyfor subjective loudness levels of the human ear. The curved lines from 0to 120 sones indicate subjective loudness. The maximum amplitude of avibrating string produces its maximum loudness. Therefore, when a stringis plucked to vibrate at its maximum loudness allowed by the logarithmicspiral curvature of the finger board, the sound power imparted to theair is inversely proportional to the frequency produced by the vibratinglength of said string.

Line 38 of FIG. 10 represents the sound power of a double bass with thelogarithmic spiral finger board, plucked at maximum loudness for allnotes. Said line is drawn at a slope that represents the establishedinverse proportionality of sound power to frequency. 'It is straightbecause of thelog-log scales of the graph. Lines 40 show sound power ofsaid double base when its strings are plucked to amplitudes less thanmaximum. The ends of these lines terminate at the usual high and lowlimits of pitch that can be produced on the instrument. Line 38 closelyfollows the constant subjective loudness line of sones, providing that astringed instrument with the logarithmic spiral finger board not onlypossesses a constant maximum plucking force but can produce a sound ofconstant subjective loudness associated with said plucking force.

The logarithmic finger board as disclosed and described makes it easierto depress the strings adjacent their points of suspension, allowsincreased amplitude of vibration of the strings intermediate theirpoints of suspension, facilitates increased usable length of the fingerboard adjacent the bridge, and provides a constant maximum pluckingforce for all active lengths of a string. As applied to a double bass,the finger board also limits the maximum subjective loudness to the samevalue for all active lengths of the string.

I claim:

. 1. In a stringed musical instrument having a nut at its top end, abridge or tail piece at its bottom end, and strings crossing andsuspended over said nut and said bridge;

a curved finger board having a top end, a bottom end, and alongitudinally inwardly curving intermediate face portion between saidtop and bottom ends;

said curved finger board being adapted to lie adjacent the strings withits top end at said nut, and its bottom end adjacent said bridge;

the longitudinal curvature of said face portion being a logarithmicspiral originating at the point where said strings cross said bridge;

said logarithmic spiral forming the face curvature of said finger boardunder each string so that at every point along its length at which saidstring is pressed to said finger board, the same angle will be formedbetween said string and said finger board.

2. In a stringed musical instrument having a nut at its top end, abridge or tail piece at its bottom end, and strings crossing andsuspended over said nut and said bridge;

a finger board having a top end, a bottom end, and an intermediate faceportion between said top and bottom ends, said intermediate face portioncontaining frets whose top contact surfaces lie on a longitudinallyinward curve;

said finger board being adapted to lie adjacent the strings with its topend at said nut, and its bottom end adjacent said bridge;

the longitudinal curve described by the top contact surfaces of saidfrets being a logarithmic spiral originating at the point where saidstrings cross said bridge;

said logarithmic spiral forming said curve under each string so that onevery fret to which said string is pressed, the same angle will beformed between said string and said curve.

References Cited UNITED STATES PATENTS 73,569 l/1868 Bishop 842741,290,177 l/19l9 GrimsOn 843 14 2,853,911 9/ 1958 Plants 84274 3,143,0288/1964 Fender 84-293 RICHARD B. WILKINSON, Primary Examiner I. F.GONZALES, Assistant Examiner US. Cl. X.R. 84314 UNITED STATES PATENTOFFICE CERTIFICATE OF CORRECTION Patent No. 3 ,478 ,631 November 18 1969Alan Robert Fisher It is certified that error appears in the aboveidentified patent and that said Letters Patent are hereby corrected asshown below:

Column 3, line 32, "spring" should read string Column 4, line 66,"requred" Should read required line 72, "1241" should read 12a Column 5,line 39, cancel "been". Column 6, line 3, "base" should read bass line8, "providing" should read proving Signed and sealed this 3rd day ofMarch 1970.

(SEAL) Attest:

Edward M. Fletcher, Jr. WILLIAM E. SCHUYLER, JR.

Attesting Officer Commissioner of Patents

